Republican Mitt Romney got a meager “bounce” from his choice of Paul Ryan as running mate, but the challenger has cut into President Obama’s lead in Florida and Wisconsin among likely voters, according to the new Quinnipiac University/CBS News/New York Times poll of swing states released Thursday.

The president maintains a 51 percent to 45 percent lead in the Big Enchilada battleground of Ohio, which is unchanged from the first edition of the survey released August 1.

In the new poll, Obama was at 49 percent, to Romney’s 46 percent, among likely voters in Florida. That compares to a 50 percent to 41 percent Obama lead earlier in the month.

And in Wisconsin, the horse race stands at 49 percent for Obama, to 47 percent for Romney, an improvement for the Republican from his 45 percent to 51 percent deficit in the August 1 survey. Ryan, the House budget chairman, represents a southeast Wisconsin congressional district.

By margins of more than 4-1, voters in each state say that the federal Medicare program of health-care for retirees is worth the cost, and six in 10 voters say they want to keep the current system in place. Ryan is most known for his budget proposal that would convert Medicare partly into a voucher-supported private insurance program.

“Gov. Mitt Romney’s pick of U.S. Rep. Paul Ryan as his running mate has made some small difference in Florida and Wisconsin, at least at this point, when voters in these three key states are asked about their presidential vote,” Peter A. Brown, assistant director of Quinnipiac University Polling Institute, said in a statement.

“Voters, however, see Ryan in a more favorable light than they do Vice President Joseph Biden. And when voters assess the two running mates’ qualifications to become president, Biden is only slightly ahead in Florida and Ohio and slightly behind the seven-term congressman in Wisconsin. In fact, Ryan’s qualified/unqualified ratio is better than Biden’s.”

Most voters agreed with Romney’s core contention that the federal government, under Obama, is trying to do too many things that ought to be left to the private sector.